9300=x^2-19x=78

Solution for 9300=x^2-19x=78 equation:

9300=x^2-19x=78

We move all terms to the left:

9300-(x^2-19x)=0

We get rid of parentheses

-x^2+19x+9300=0

We add all the numbers together, and all the variables

-1x^2+19x+9300=0

a = -1; b = 19; c = +9300;
Δ = b2-4ac
Δ = 192-4·(-1)·9300
Δ = 37561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-\sqrt{37561}}{2*-1}=\frac{-19-\sqrt{37561}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{37561}}{2*-1}=\frac{-19+\sqrt{37561}}{-2}
$